On the Rationalization of Sight by William M. Ivins, Jr. (review)

158 Books effect of accidental gene recombinations in germ cells, but also the impact on the inherited structures of unique sensory histories' (p. 219). In a sense probably not meant by the author, the last phrase could mean that there is feedback from sensory experience to the gene. Geneticists claim that these innate deep structures are the outcome of selection. Yet someof them have little survival value; they do not contribute to homeostasis. Another point is that humans have not existed long enough for the selection process to have achieved such universality over such a wide population.The brain sciences appear to be establishing the view that human cultural progress has been accelerated by feedback to the genes during ontogenetic development. This is one example of the kind of fundamental question raised by the book. It incorporates much of the most recent brain research, though some, like the work of Colin Blakemore at Cambridge (U.K.), is not acknowledged. The Language of Mathematics. Frank Land. John Murray. London, 1975. 264 pp., illus. Paper, f1.25. Reviewed by G. Stanley Smith* This large-format paperback is a re-issue of the book originally published in 1960.Since there have been several reprints, one can infer that its popularity has been well established. Attractively presented with numerous two-colour drawings, it is a real bargain- made possible, as appears from a remark in the preface, through the co-operation of the Shell International Petroleum Company. Its main purpose is to stimulate those who may have considered mathematics a distasteful and unnecessary study to explore the subject and perhaps to experience some unexpected delights. They will find in the book that even the most elementary operations in arithmetic, algebra and geometry are explained with great clarity and with apt illustrations. As a bonus, many odd bits of information will be collected on the way, such as the fact that the average silkworm produces 450 metres of thread (introduced to explain the derivation of the denier unit for silk or nylon thread). In a useful section on statistics. one is gently led through the ideas of distributions, histograms and standard deviation to correlation, significance tests, ways of studying reliability and validity of results and methods of assessing probability. At the end one should be in a better position to understand the special terms of statistical inference that permeate various branches of knowledge. Historical background is prominent, particularly in the sections on number systems and how they have developed, units of length. weight, capacity and money, and time and the calendar. New units, including those for money in Britain, are not introduced. so certain calculations involving money at various places in the book have an out-of-date appearance. Readers who are not altogether ignorant of mathematics will skip large portions of the text, but they are likely to be forced to a halt when, for instance, the author brings together the number of teams in the last five rounds of the British Football Association Cup, the successive frequencies of theC notes on a piano, and the profile of organ pipes to illumine exponential curves. With all the wealth of illustrative diagrams and clear expositions, an artist feeling in need of some mathematical bases for his work will find considerable help, particularly in the sections on geometry, topology and the golden section. The chapter on the Fibonacci sequence and the golden section is one of the best short treatments of the subject that I have read. It seemsa pity, however, that, after 15years, the author has not taken the opportunity to reflect some of the more recent changes in the presentation of mathematics by teachers in relation to the theory of sets and groups (somewhat inadequately represented here in two or three pages), matrices (not even referred to) and general structural ideas in algebra. But, I suppose. one cannot have everything in this very enjoyable book. Thinking Machines: A Layman's Introduction to Logic, Boolean Algebra, and Computers. Revised and enlarged edition Irving Adler John Day, New York, 1974 Reviewed by James Gip** *3 Marine Drive, Seaford, Sussex, England ~~~ _ _ _ _ _ Adler begins his book with a brief discussion of some of...